Frequent pattern mining algorithms often draw on graph isomorphism to identify common pattern occurrences. Recent research, however, has focused on cases in which patterns can differ from their occurrences. Such cases have great potential for the analysis of noisy network data. This approach can be refined still further, though. Most existing FPM algorithms consider differences in edges and their labels, but none of them so far has considered the structural differences of vertices and their labels. Discerning how to identify cases that differ from the initial pattern by any number of vertices, edges, or labels has become the main challenge in this approach. As a solution, we suggest a novel Frequent Pattern Mining (FMP) algorithm named Mining Frequent Patterns (MFP) with two central new characteristics. First, we begin by using the inexact matching technique, which allows for structural differences in edge, vertices, and labels. Second, we follow the approximate matching with a focus on mining patterns within the directed graph, as opposed to the more commonly explored case of patterns being mined from the undirected graph. Our results illustrate the effectiveness of this new MFP algorithm in identifying patterns within an optimized time.